Transcript Reading Quiz - Work & Energy

Reading Quiz - Work & Energy
1. A woman holds a bowling ball in a fixed
position. The work she does on the ball
___ 1. depends on the weight of the ball.
___ 2. cannot be calculated without more
information.
___ 3. is equal to zero.
2. A man pushes a very heavy load across
a horizontal floor. The work done by gravity
on the load
___ 1. depends on the weight of the load.
___ 2. cannot be calculated without more
information.
___ 3. is equal to zero.
3. When you do positive work on a
particle, its kinetic energy
___ 1. increases.
___ 2. decreases.
___ 3. remains the same.
___ 4. need more information about the
way
the work was done
4. The gravitational potential energy of a
particle at a height z above Earth’s
surface
___ 1. depends on the height z.
___ 2. depends on the path taken to bring
the
particle to z.
___ 3. both 1 and 2.
___ 4. is not covered in the reading
assignment.
5. Which of the following is not a
conservative force?
___ 1. the force exerted by a spring on a
particle in one dimension
___ 2. the force of friction
___ 3. the force of gravity
___ 4. not covered in the reading
assignment
Work
• Work done by a constant force on an object:
W  Fd cos
where F = magnitude of constant force
d = magnitude of the displacement
 = angle between the force and
displacement vectors
• Graphical interpretation of work
• Work done by a variable force.
Conceptual Questions
1) A box slides through a distance of 3 m on a rough
floor where the force of friction is 10 N. What is
the work done on the box?
____ a) 0 N·m
____ b) +30 N·m
____ c) - 30 N·m
____ d) +0.30 N·m
____ e) - 0.30 N·m
2) The moon revolves around the earth in a
circular orbit, kept there by the gravitational
force exerted by the earth. Gravity does
___ a) positive work
___ b) negative work
___ c) no work
___ d) variable work
on the moon.
What evidence do you have to support your
answer?
3) The figure shows four situations in which a force
acts on a box while the box slides to the right a
distance d across a frictionless floor. The
magnitudes of the forces are identical. Rank the
situations according to the work done on the box
during the displacement, from most positive to
most negative.
Quantitative Questions
1) Find the work done by the force of gravity when
an object of mass m is raised from a height of y
meters to a height of y+h meters.
2) A spring is a device where the force it exerts is
directly proportional to its displacement from its
natural (unstretched) length. The constant of
proportionality is called the spring constant k.
Draw a graph of the spring force versus its
displacement. What is the work done in
stretching a spring from its natural length by an
amount x?
3) A 280 kg piano slides 4.3 m down a 30 incline
and is kept from accelerating by a man who is
pushing back on it parallel to the incline. The
effective coefficient of kinetic friction is 0.40.
Calculate: (a) the force exerted by the man, (b) the
work done by the man on the piano, (c) the work
done by the friction force, (d) the work done by the
force of gravity, and (e) the net work done on the
piano.
Energy
• Energy - property that gives something the
capacity to do work. Three broad categories:
- Kinetic energy
- Potential energy
- Rest energy
• Kinetic Energy - Energy related to motion:
KE  1 mv2
(definition)
2
• Potential Energy - Energy related to position.
• Rest Energy - Energy by virtue of the mass
of an object: Eo  moc2
Work-Energy Principle
• The net work done on an object is always
equal to the change in its kinetic energy:
Wnet KE  KEf  KEi
• Conservative forces: work done by these
forces are independent of path; they depend
only on the end points. Examples include
gravitation, spring and magnetic forces.
• It is meaningful to define an associated
potential energy only for conservative forces.
Quantitative Problems
1) An automobile traveling 60 km/h can brake
to a stop within a distance of 20 m. If the car
is going twice as fast, 120 km/h, what is its
stopping distance? The maximum braking
force is approximately independent of speed.
2) A 600 gram hammer head strikes a nail at a
speed of 4.0 m/s and drives it 5.0 mm into a
wooden board. What is the average force on
the nail?
3) A crate of mass 10 kg is pulled up a rough
incline with an initial speed of 1.5 m/s. The
pulling force is 100 N parallel to the incline,
which makes an angle of 20° with the
horizontal. If the coefficient of kinetic friction is
0.4, and the crate is pulled a distance of 5 m, (a)
how much work is done against gravity? (b)
How much work is done against friction? (c)
How much work is done by the 100 N force? (d)
What is the change in kinetic energy of the
crate? (e) What is the speed of the crate after
being pulled 5 m?
Potential Energy
• For every conservative force, we can define a
potential energy function. The change in the
potential energy is equal to the negative of the
work done by the conservative force:
PE f  PEi Wi f
• Examples: gravitational PE = mgh
elastic PE = 12 kx2
• Note: Cannot define a potential energy function
for a non-conservative force.
Conservation of Mechanical Energy
• Net work done by net force which equals
the vector sum of conservative and nonconservative forces, implying: Wnet WC WNC
• Since Wnet KE , and WC PE , the above
reduces to: WNC KE PE - the general
form of the work-energy principle.
• If only conservative forces are acting, or if
the work done by the non-conservative
forces present is zero, i.e. WNC  0 , then
KE PE  0 or KEi  PEi  KE f  PE f
Conceptual Question
Two water slides at a pool are shaped differently but
start at the same height h. Two riders, Paul and
Kathleen, start from rest at the same time on
different slides.
Which rider, Paul or Kathleen, is travelling faster at
the bottom and who gets there first?
___ a) Paul & Paul
___ e) same & Paul
___ b) Paul & Kathleen
___ f) same & Kathleen
___ c) Kathleen & Paul
___ g) Paul & same
___ d) Kathleen & Kathleen ___ h) Kathleen & same
Quantitative Problems
1) A small mass m slides without friction along the
looped apparatus show. If the object is to remain
on the track, even at the top of the circle (whose
radius is r), from what minimum height h must it
be released?
2) A roller coaster is pulled up to point A where it is
released from rest. Assuming no friction, calculate
the speed at points B, C and D. Now suppose the
roller coaster passes point A with a speed of 1.70
m/s. If the average force of friction is equal to one
fifth of its weight, with what speed will it reach
point B? The distance traveled is 45.0 m.
3) A ball is attached to a horizontal cord of length L
whose other end is fixed. (a) If the ball is released,
what will be its speed at the lowest point of its
path? (b) A peg is located a distance h directly
below the point of attachment of the cord. If h =
0.80L, what will be the speed of the ball when it
reaches the top of its circular path about the peg?
4) The figure shows an 8 kg stone at rest on
a spring. The spring is compressed 10.0
cm by the stone. (a) What is the spring
constant? (b) The stone is pushed down an
additional 30.0 cm and released. What is
the elastic potential energy of the
compressed spring just before that
release?
(c) What is the change in the gravitational
potential energy of the stone-Earth system
when the stone moves from the release
point to its maximum height? (d) What is
that maximum height, measured from the
release point?
Conservation of Energy; Power
• The law of conservation of energy is one of the
most important principles of physics. It states:
The total energy is neither increased nor
decreased in any process. Energy can be
transformed from one form to another,
and transferred from one body to another,
but the total amount remains constant.
• Power: rate of doing work (or transforming
energy). Hence average power is
P  work (energy transformed)  Fv
time
Discussion Problems
1) Other than nuclear energy, why do we say
the source of all energy comes from the
sun? Specifically, what about:
(a) wind energy
(b) hydro-electricity
(c) fossil fuel - coal, wood, oil, gas
(d) food that we eat
2) To accelerate your car at a constant
acceleration, the car’s engine must
____ a) maintain a constant power output
____ b) develop ever-decreasing power
____ c) develop ever-increasing power
____ d) maintain a constant turning speed
3) Compared to yesterday, you did 3 times the
work in one-third the time. To do so, your
power output must have been
____ a) the same as yesterday’s power output
____ b) one-third of yesterday’s power output
____ c) 3 times yesterday’s power output
____ d) 9 times yesterday’s power output